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Key Rate Durations

Can you guys explain why PO strips have negative key rate durations in the short term while interest only strips start out with positive key rate durations?

Thanks!

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An IO strip is a bond and if the mortgages were not prepayable it would behave just like any other bond with positive key rate durations all along the yield curve. Alas, mortgages are prepayable and that means that IO strips have negative effective durations. This is because when interest rates drop, people refinance and the total amount of cash paid to the IO holder drops. The decreased cash flow trumps the decreased discount rate every time.

Key rate durations measure the sensitivity at points along the yield curve. We use them for assessing non-parallel shifts in the curve. Imagine that you own IO strips and the <= 1 year rates drop but other rates stay the same. This is good for you, because you own a bond and interest rates dropped. A drop in <= 1 year interest rates does nothing to the refinance rate because it does not affect mortgage rates. However, out around (uh, I don’t really know) 7 years or so the drop in interest rates will cause people to refinance so the krd becomes negative.

PO strips with negative key rate durations….Hmmm….

Edit: I don’t think a PO strip has any negative key rate durations.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

They do according to Schweser Book 3 pg 112. “Principal-only strips have negative key rate durations in the short and intermediate rates, which turn positive for longer rates (eg 10 year).

the cfai text has a graph that displays -ve durations for PO as well.

I think it’s just wrong. I can’t think of any reason why a PO strip would have any negative krd’s. I think a PO strip has similar krd to the underlying pool at short maturities and much higher krd’s at high maturities.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

Have to agree with JDV here, sometimes CFAI is talking out of their a** without explaining why it would be so.

If everything else is held constant - key rate duration should be positive.

We need someone who has actually traded a mortgage derivative on board. CSK - have you ever traded one? (I haven’t).

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

I asked my friend who works with MBS, i will let you guys know if i hear anything

PO has negative key rate duration in the short and intermediate term and turn to positive key rate duration in the longer term. which because when yield falls, people hold MBS more like to refinance, and prepay the principle, which caused PO MBS value underperform compared to bullet bond, but for older PO MBS, the MBS holder may not refinace due to the less loan left at the end. when yiled increase the PO will perform the same as bullet bond.

IO start with postive key rate duration and turn to negative. because for new issued IO, if the yield decrease, the MBS holder finance, and the IO vaue based on the interest income according to the principle balance, so the IO value falls, however, the yield increase, the IO value increase due to the higher loan balance. for the longer term IO MBS people unlikely refinance even if the key rate change due to the less mortgage loan.

Negative rate duration implies the MBS value changes the same direction as the changes in key rate (interest).

?

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

the above explaination combine the Schweser MBS (yiled cureve risk) and CFAI curriculum.

Do you know what key rate duration means?

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

They are indeed negative, but I have only confirmed this through the our FI analytics software. If you were to graph the KRDs, the positive values which are located near the maturity date significantly outweigh the negative krds at the shorter buckets. I’m talking like -.1 KRD1 vs. 13 KRD10 for one particular PO.

Why is it negative?

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

Joey, if I knew, you would be the first person I would tell… In reality I don’t know the answer (the MBS PMs here probably wouldn’t know either). All I am doing is pointing to the way citi models their zeros coupon bonds. I know it’s not adding much…

OK - I’m on a mission to find out.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

Hmm..

Found this:
http://books.google.com/books?id=S4YGyb506wMC&pg=PA172&lpg=PA172&dq=%22k...

So it’s from Thomas Ho (really smart guy). They also credit Donald Chambers who is my mentor and friend, so I’ll talk to him this evening and see if he knows (he won’t, but always good to talk to Uncle Donnie).

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

Joey did you get the chance to talk to the guy?

Oops. Will do. Sorry.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

baocarol Wrote:
——————————————————-
> PO has negative key rate duration in the short and
> intermediate term and turn to positive key rate
> duration in the longer term. which because when
> yield falls, people hold MBS more like to
> refinance, and prepay the principle, which caused
> PO MBS value underperform compared to bullet bond,
> but for older PO MBS, the MBS holder may not
> refinace due to the less loan left at the end.
> when yiled increase the PO will perform the same
> as bullet bond.
>
I thought PO acts like discount bonds, you buy them 90, 95 cents on the dollar. Therefore, I would think when rate drops, people are more likely to refi, therefore principle gets returned faster. Therefore, we can observe a price increase in PO. That is still positive key rate duration.

They are essentially zeros, but with exposure to prepayments. You are correct in that the value of a PO will rise as rates fall (higher prepayment speeds lead to earlier return of principal), but that does not mean that the KRDs are all positive. Some of the lower KRDs are negative according to our readings, however the much larger (in absolute terms) and positive KRDs near the maturity date dominate.

ws Wrote:
——————————————————-
> baocarol Wrote:
> ————————————————–
> —–
> > PO has negative key rate duration in the short
> and
> > intermediate term and turn to positive key rate
> > duration in the longer term. which because when
> > yield falls, people hold MBS more like to
> > refinance, and prepay the principle, which
> caused
> > PO MBS value underperform compared to bullet
> bond,
> > but for older PO MBS, the MBS holder may not
> > refinace due to the less loan left at the end.
> > when yiled increase the PO will perform the
> same
> > as bullet bond.
> >
> I thought PO acts like discount bonds, you buy
> them 90, 95 cents on the dollar. Therefore, I
> would think when rate drops, people are more
> likely to refi, therefore principle gets returned
> faster. Therefore, we can observe a price
> increase in PO. That is still positive key rate
> duration.

That’s positive effective duration (or something). Key rae durations depend on moving a particular yield (like 3 months).

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

I know that…however, I when I read the material on CFAI and Schweser, looked at the chart, still doesn’t make a whole lot sense to me, since there was a lack of detailed explanation. I am eager to find out too.

ymmt Wrote:
——————————————————-
> They are essentially zeros, but with exposure to
> prepayments. You are correct in that the value of
> a PO will rise as rates fall (higher prepayment
> speeds lead to earlier return of principal), but
> that does not mean that the KRDs are all positive.
> Some of the lower KRDs are negative according to
> our readings, however the much larger (in absolute
> terms) and positive KRDs near the maturity date
> dominate.

I think I somewhat know what you mean. So, for shorter term (loan is about to mature, ie, I have 3 years left on my mortgage), even there is a rate drop, people are LESS likely to refi because loan is about to mature (less time). For longer term (ie. I have another 15 years left on my mortgage), with a rate drop, people are MORE likely to refi.

Even with people LESS likely to refi with only few years left on their mortage, I am still puzzled that why would a PO move in the same direction with rate??? Because at this point, since people are less likely to refi, the prepayment risk is reduced, they will act MORE like a zero.

Thanks

I think I know what this is. Holding PO strips is like holding call options on long-term bonds. In fact, the only reason that they have such high effective duration is that mortgage holders hold calls and by buying PO strips you are buying that optionality. That means for early krd’s, the interest rate sensitivity is like rho of the bond call. That gives the negative krd for short maturities and macthes up pretty well with the magnitudes given by ymmt’s desk.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

ws Wrote:
——————————————————-
> ymmt Wrote:
> ————————————————–
> —–
> > They are essentially zeros, but with exposure
> to
> > prepayments. You are correct in that the value
> of
> > a PO will rise as rates fall (higher prepayment
> > speeds lead to earlier return of principal),
> but
> > that does not mean that the KRDs are all
> positive.
> > Some of the lower KRDs are negative according
> to
> > our readings, however the much larger (in
> absolute
> > terms) and positive KRDs near the maturity date
> > dominate.
>
>
> I think I somewhat know what you mean. So, for
> shorter term (loan is about to mature, ie, I have
> 3 years left on my mortgage), even there is a rate
> drop, people are LESS likely to refi because loan
> is about to mature (less time). For longer term
> (ie. I have another 15 years left on my mortgage),
> with a rate drop, people are MORE likely to refi.
>
> Even with people LESS likely to refi with only few
> years left on their mortage, I am still puzzled
> that why would a PO move in the same direction
> with rate??? Because at this point, since people
> are less likely to refi, the prepayment risk is
> reduced, they will act MORE like a zero.
>
> Thanks

I think we are talking about krd for PO’s from newly minted long-term mortgage pools. At least the Ho article above gives PO krd for PO’s from a brand new GNMA pool. If there is 3 years left in a GNMA pool, the remaining interest and principal are nearly insignificant (there literally might only be 6 mortgages remaining in the pool).

I know that in GNMA pool #1, there were only 3 mortgages that made it to final maturity. Since they had been paying down principal all along, the total amount of the pool was like a car loan with three years left.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!

I can see you comparing bond call with PO, but are you saying bond call has negative krd at the short end? and why is that?

That’s what ymmt’s desk says and what Thomas Ho says, so it’s sounding pretty credible to me. Unless someone can come up with a better idea, I think it is just the usual option rho looking like a key rate duration.

I’m Da Church of the faithful, I’m Liao Fengyi, clergywoman mother should have to introduce you to me, I have seen you twice, in which time you are more impressed with everyone I guess in the back of the church at noon to eat noodle face!